P10-36 (similar to) Question Help * The WLJ Boat Company, which is under contrac
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P10-36 (similar to) Question Help * The WLJ Boat Company, which is under contract to the U.S. Navy, assembles troop deployment boats. As part of its research program, it completes the assembly of the first of a new model (PT109) of deployment boats. The Navy is impressed with the PT109. It requests that WLJ Boat submit a proposal on the cost of producing another six PT109sWLJ Boat reports the following cost information for the first PT109 assembled WLJ Boat uses a 90% ncremental unit time learning model as a basis for predicting direct manufacturing labor-hours in its assembling operations. (A 90% learning curve means b·-0.152004.) (Click the icon to view the cost information.) Read the requirements Requirement 1. Prepare a prediction of the total costs for producing the six PT 109s for the Navy. Begin by calculating the cumulative total time in labor-hours. (Round the individual unit time for Xth unit to the nearest whole number.) Number of Individual unit time for Cumulative total time: units Xth unit: Labor-hours Data Table Direct material Direct manufacturing labor time for first boat Direct manufacturing labor rate Variable manufacturing overhead cost Other manufacturing overhead Tooling costs Learning curve for manufacturing labor time per boat $202,000 15,700 labor-hours $46 per direct manufacturing labor-hour $29 per direct manufacturing labor-hour 15% of direct m anufacturing labor costs $282,000 90% incremental unit-timeb Tooling can be reused at no extra cost because all of its cost has been assigned to the first deployment boat In 0.90 0.105361 .693147 b Using the formula for a 90% learning curve. 0.152004 Print DoneExplanation / Answer
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Calculation of the direct manufacturing labor-hours b= -0.152004 90% LC to produce the 2nd to 7th boats can be calculated Individual as follows: y = aXb (to the power of b) where Cumulative Unit Time for Cumulative y = Time (in labor-hours) to produce the most recent unit # of Xth Unit (y) Total Time: a = labor hours required for first unit Units Labor-Hrs. Labor-Hrs. X = cumulative number of units y=aXb 1 15,700 15,700 b = ln(learning-curve % in decimal form) / ln2 2 14,130 29,830 b = ln 0.90 / ln2 = -0.152004 3 13,285 43,115 4 12,717 55,832 5 12,293 68,125 6 11,957 80,082 7 11,680 91,762 The DLHs required to produce the 2nd through the 7th boats 76,062 Incremental Unit-time Learning Cost to produce the 2nd through 7th boats Model Direct materials, 6 X $202,000 $1,212,000 Direct manufacturing labor (DML) $3,498,852 Variable mfg. Overhead $2,205,798 Other mfg. Overhead (15% of DML$) $524,828 Total costs for boats 2 through 7 $7,441,478 2. Compare the cost of the 2nd - 7th boats using the "Incremental Unit-time Learning Model" with the costs of the 2nd - 7th boats using the "Cumulative Average-time Learning Model: DLH Req 76,062 66,060 Incremental Cumulative Unit-time Learning Average-time Cost to produce the 2nd through 7th boats Model Learning Model Direct materials, 6 X $202,000 $1,212,000 $1,212,000 Direct manufacturing labor (DML) (DLH x rate) $3,498,852 $3,038,760 Variable mfg. Overhead (DLH x rate) $2,205,798 $1,915,740 Other mfg. Overhead (15% of DML$) $524,828 $455,814 Total costs for boats 2 through 7 $7,441,478 $6,622,314 Difference ($819,164) Why are the predictions different? The incremental unit-time learning curve has a slower rate of decline in the time required to produce successive units than does the cumulative average-time learning curve even though the same 90% factor is used for both curves. The reason is that, in the incremental unit-time learning model, as the number of units double, only the last unit produced has a time of 90% of the initial time. In the cumulative average-time learning model, doubling the number of units causes the average time of all the additional units produced (not just the last unit) to be 90% of the initial time. Cumulative Incremental Average-time Unit-time Learning Learning Model Model Cumulative Cumulative Cumulative # of Total Time: Total Time: Units Labor-Hrs. Labor-Hrs. 1 15,700 15,700 2 28,260 29,830 3 39,856 43,115 4 50,868 55,832 5 61,464 68,125 6 71,741 80,082 7 81,760 91,762 How should WLJ Boat decide which model it should use? The company should examine its own internal records on past jobs and seek information from engineers, plant managers, and workers when deciding which learning curve better describes the behavior of direct manufacturing labor-hours on the production of the PT109 boats.Related Questions
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